Reintroducing the Second Player in EPR

19 pages•Published: October 23, 2026

Leroy Chew, Mikoláš Janota, Miroslav Olšák and Martin Suda

Abstract

We present a PSPACE-complete fragment of first order logic we call QEALM (QBF-like EPR by Alternating Level-ordered Miniscoping). Unlike other well-known fragments it is more analogous to QBF (Quantified Boolean Formulas) because it has game-like alternations and can be restricted to complete problems for the polynomial hierarchy. QEALM is a natural first order analogue to QBF just as EPR (Effectively Propositional logic) is a first analogue to Dependency QBF.
In this paper we prove the PSPACE and Polynomial Hierarchy completeness theorems of QEALM among other nice properties such as closure under Robinson's resolution and retained hardness after intersection with Schaefer fragments. We use our new definition to identify problems in the TPTP library that fall into this fragment and their level in the polynomial hierarchy.

Keyphrases: epr, pspace, qbf, schaefer fragments

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 61-79.

Links:	https://easychair.org/publications/paper/4vvj
	https://doi.org/10.29007/sfg8

BibTeX entry

@inproceedings{LPAR-26:Reintroducing_Second_Player_EPR,
  author    = {Leroy Chew and Mikoláš Janota and Miroslav Olšák and Martin Suda},
  title     = {Reintroducing the Second Player in EPR},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/4vvj},
  doi       = {10.29007/sfg8},
  pages     = {61-79},
  year      = {2026}}

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